Why does Simulated Annealing not take worse solution if the energy difference becomes higher?
Note that you can't really predict whether your escape from a local minimum will work or not - you might just wind up in another, worse local minimum. The probability function you describe increases the likelihood of this happening. By upweighting the likelihood of allowing small energy differences, you allow for the possibility of escaping local minima, while ensuring that whatever new minimum you find can't be that much worse that where you started. If you make the acceptance of large energy differences more likely, you can escape local minima more often, but you increase the likelihood that you'll just wind up in a region with an even higher local minimum.